Tag: free, forced and damped oscillations

Questions Related to free, forced and damped oscillations

The oscillation of a body or system with its own natural frequency and under no external influence other than the impulse that initiated the motion

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. Damped oscillation

  2. Free oscillation

  3. Impulsive oscillation

  4. None of these

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Correct Option: B
Explanation:

Force vibration is a type at vibration in which a body is vibrate without any external influence and vibrates with its natural frequency. So, given statement describes a free vibrations.


The vibrations which occur when work is being done on the system are called 

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. free vibrations.

  2. forced vibrations.

  3. natural vibrations.

  4. random vibrations.

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Correct Option: B
Explanation:

The vibrations which occur when work is being done on the system is called forced vibration.

Motion of reciprocating pistons in engine is an example of

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. Forced vibration

  2. Natural vibration

  3. Recursive vibration

  4. None of these

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Correct Option: A
Explanation:

A motion of reciprocating pistons in an engine is an example of force vibration. In this case motion of the piston is governed by a pressure of a gas inside ignition of a chamber.

The motion of a vehicle suspension system just after the vehicle encounters a pothole is an example of 

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. natural vibration

  2. damped vibration

  3. forced vibration

  4. None of these

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Correct Option: A
Explanation:

The motion of a vehicle suspension system just after the vehicle encounters a pothole is an example of natural vibration. When suspension system encounters a pothole it is disturbed from its equilibrium position after that an oscillatory motion generates inside it to take it back its initial position but there is no external force which maintains that oscillatory motion.

Assertion : A child in a garden swing periodically presses his feet against the ground to maintain the oscillations.
Reason : Then all free oscillations eventually die out because of the ever present damping force.

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. If both assertion and reason are true and reason is the correct explanation of assertion.

  2. If both assertion and reason are true and reason is not the correct explanation of assertion.

  3. If assertion is true but reason is false.

  4. If both assertion and reason are false.

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Correct Option: A
Explanation:

The free oscillation of a body or system is due to its own natural frequency and under no external influence. But to carry out it continuously, the external impulse is needed. The child is doing this by pressing the ground.

Obviously, in the absence of such external impulse or force, free oscillations will die soon due to other negative forces i.e. damping forces.

Therefore assertion and reason both are correct and the reason is the correct explanation of assertion.

 

Option A is correct.

A linear harmonic oscillator of force constant $2 \times$10$^{6}$Nm$^{-1}$ and amplitude 0.01 m has a total mechanical energy of 160 J. Its

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. maximum potential energy is 100 J

  2. maximum kinetic energy is 100 J

  3. maximum potential energy is 160 J

  4. minimum potential energy is zero.

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Correct Option: B,C
Explanation:

As, we know total mechanical energy $=$ maximum potential energy

$\therefore \quad ATQ.T.E=160J\Rightarrow Max.P.E.=160J$
$\Rightarrow$  Statement (C) is correct.
Also, for maximum kinetic energy, we know,
$K.E.=\dfrac { 1 }{ 2 } K\left( { x } _{ m }^{ 2 } \right) $
where ${ x } _{ m }=\left( 0.01 \right) m\quad & \quad K=2\times { 10 }^{ 6 }{ Nm }^{ -1 }$
$\Rightarrow K.E.=\left( \dfrac { 1 }{ 2 }  \right) \left( 2\times { 1 }0^{ 6 } \right) { \left( 0.01 \right)  }^{ 2 }=100J$
$\Rightarrow$  Statement (B) is the correct answer.

What impulse need to be given to a body of mass $m$, released from the surface of earth along a straight tunnel passsing through centre of earth, at the centre of earth, to bring it to rest(Mass of earth $M$, radius of earth R) 

physics oscillations introduction to sound free, forced and damped oscillations resonance

  1. $m \sqrt { \dfrac { G M } { R } }$

  2. $\sqrt { \dfrac { G M m } { R } }$

  3. $m \sqrt { \dfrac { G M } {2 R } }$

  4. $zero$

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Correct Option: D

A particle is suspended from a light vertical inelastic string of length 'l' from a fixed support. At its equilibrium position, it is projected horizontally with a speed $\sqrt{6gl}$. Find the ratio of tension on string, its horizontal position to that in vertically above the point of support.

physics oscillations introduction to sound free, forced and damped oscillations resonance

  1. $2:1$

  2. $4:1$

  3. $3:1$

  4. $5:1$

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Correct Option: B

The amplitude of a damped harmonic oscillator becomes halved in $\ minute$. After three minutes, the amplitude will becomes $\dfrac{1}{x}$ of initial amplitude, where $x$ is ?

physics oscillations introduction to sound free, forced and damped oscillations resonance

  1. $8$

  2. $2$

  3. $3$

  4. $4$

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Correct Option: A

A particle performing SHM is found at its equilibrium at $  t=1\ sec$ and it is found to have a speed of $0.25 \mathrm{m} / \mathrm{s}  $ at $  \mathrm{t}=2\ \mathrm{sec}  $ . If the period of oscillation is $6\ \mathrm{sec}  $. Calculate amplitude of oscillation

physics oscillations introduction to sound free, forced and damped oscillations resonance

  1. $ \frac{3}{2 \pi} \mathrm{m} $

  2. $ \frac{3}{ \pi} \mathrm{m} $

  3. $ \frac{6}{2 \pi} \mathrm{m} $

  4. $ \frac{6}{ \pi} \mathrm{m} $

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Correct Option: A